Poststratification and Conditional Variance Estimation

Abstract

Post-stratification estimation is a technique used in sample surveys to improve efficiency of estimators. Survey weights are adjusted to force the estimated numbers of units in each of a set of estimation cells to be equal to known population totals. The resulting weights are then used in forming estimates of means or totals of variables collected in the survey. For example, in a household survey the estimation cells may be based on age/race/sex categories of individuals and the known totals may come from the most recent population census. Although the variance of a post-stratified estimator can be computed over all possible sample configurations, inferences made conditionally on the achieved sample configuration are desirable. Theory and a simulation study using data from the U.S. Current Population Survey are presented to study both the conditional bias and variance of the post-stratified estimator of a total. The linearization, balanced repeated replication, and jackknife variance estimators are also examined to determine whether they appropriately estimate the conditional variance.

About the benefits of poststratification in forest inventories

“…In sampling a nonrectangular area, variability of the sample size will further be increased depending on the irregularity of the particular shape of the area. With poststratification there is an additional variability of sample sizes within strata (Valliant 1993).…”

“…In the ideal case this additional information comprises the true strata weights, which might be known from previous work or other external data sources (Cochran 1977;Smith 1991;Valliant 1993). As with a priori stratification, poststratification can be based on one or more classification variables defining the strata.…”

“…Usually, it is discussed as a method supposed to increase precision (Cochran 1977;Valliant 1993;Stehman et al 2003), because it reduces selection biases by reweighting after sample selection (Smith 1991;Little 1993;Rao et al 2002). Since systematic sampling might be expected to come closer to proportional allocation than simple random sampling, one might conjecture that the relative increase in precision by poststratification will be larger with simple random than with systematic sampling.…”

“…However, although the variance of a poststratified estimator can be computed unconditionally (i.e., across all possible realizations of within strata sample sizes), inferences made conditionally on the achieved sample configuration are desirable (Valliant 1993). The conditional variance of the poststratified mean, that is the variance given the within strata sample sizes…”

Comparaison d'estimateurs de la ressource forestière tropicale basés sur plan de sondage et sur modèle compte tenu d'une post-stratification

“…Le L'estimateur qui serait a priori bien adapté à ce type de sondage serait donc un estimateur du total pour un sondage systématique simple à un degré où les unités secondaires sont post-stratifiées. Toutefois, l'expression de la variance de cet estimateur n'est pas simple [14] suivie.…”